Alternating Current Electrokinetic Motion of Colloidal Particles on

Mar 5, 2008 - ... field approximation (E = Vfluid/πr) and assuming force balance with Stokes ..... We plan further studies to determine capacitance v...
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Anal. Chem. 2008, 80, 2832-2841

Alternating Current Electrokinetic Motion of Colloidal Particles on Interdigitated Microelectrodes Seungkyung Park and Ali Beskok*

Aerospace Engineering Department, Old Dominion University, Norfolk, Virginia 23529

Alternating current (ac) electrokinetic motion of colloidal particles suspended in an aqueous medium and subjected to a spatially nonuniform ac electric field are examined using a simple theoretical model that considers the relative magnitudes of dielectrophoresis, electrophoresis, ac-electroosmosis, and Brownian motion. Dominant electrokinetic forces are explained as a function of the electric field frequency, amplitude, and conductivity of the suspending medium for given material properties and geometry. Parametric experimental validations of the model are conducted utilizing interdigitated microelectrodes with polystyrene and gold particles and Clostridium sporogenes bacterial spores. The theoretical model provides quantitative descriptions of ac electrokinetic transport for the given target species in a wide spectrum of electric field amplitude and frequency and medium conductivity. The presented model can be used as an effective framework for design and optimization of ac electrokinetic devices. With the advancement of microfabrication methods, ac electrokinetic techniques such as electrophoresis (EP), dielectrophoresis (DEP) and ac electroosmosis (ac-EO) have been widely investigated and utilized for separating, sorting, mixing, and detection of colloidal particles and biological species on microscale devices.1-8 Alternating current electrokinetic techniques provide a great potential for development of micro total analysis systems (µ-TAS). Because colloidal motion is mainly induced by interaction with an ac electric field, manipulation of submicrometer scale particles without mechanical moving parts is possible, and the direction and magnitude of the colloidal motion can be controlled by adjusting the frequency and amplitude of the applied electric field.9 Moreover, ac electrokinetic techniques are well suited for * Corresponding author. Ali Beskok, Phone: (757) 683-6818. Fax: (757) 6833200. E-mail: [email protected]. (1) Pethig, R.; Markx, G. H. Trends Biotechnol. 1997, 15, 426. (2) Wong, P. K.; Wang, T.-H.; Deval, J. H.; Ho, C.-M. IEEE/ASME Trans. Mechatronics 2004, 9, 366. (3) Cheng, J.; Sheldon, E. L.; Wu, L.; Uribe, A.; Gerrue, L. O.; Carrino, J.; Heller, M. J.; O’Connell, J. P. Nat. Biotechnol. 1998, 16, 541. (4) Gascoyne, P.; Mahidol, C.; Ruchirawat, M.; Satayavivad, J.; Watcharasit, P.; Beckera, F. F. Lab Chip 2002, 2, 70. (5) Hughes, M. Electrophoresis 2002, 23, 2569. (6) Kralj, J. G.; Lis, M. T. W.; Schmidt, M. A.; Jensen, K. F. Anal. Chem. 2006, 78, 5019. (7) Rosenthal, A.; Voldman, J. Biophys. J. 2005, 88, 2193. (8) Taff, B. M.; Voldman, J. Anal. Chem. 2005, 77, 7976. (9) Gascoyne, P.; Vykoukal, J. Electrophoresis 2002, 23, 1973.

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integration with other electronic components on a single chip with a small foot print area.10 However, ac electrokinetic manipulation of colloidal particles is generally limited by the applicable electric field conditions and relative polarizability of the suspending medium compared to that of the particles and electrodes. Accordingly, the design and optimization process of ac electrokinetic devices require performance prediction and validation over specific operational ranges of the electric field, which should be considered as a function of the electrode geometry, and electromechanical properties of the target species and suspending medium. For example, when the size and properties of the target species are fixed, DEP forces can be represented as a function of the ionic strength of media, electric field frequency and amplitude, and the electrode geometry. In order to utilize DEP for manipulating colloidal particles, the magnitude of the DEP force should be large enough to dominate other forces. If this is induced using large electric fields, electrolysis of the suspending medium can occur.11 Relative polarizability of the suspending medium can be controlled by adjusting the molarity of the buffer solution to vary the direction and magnitude of DEP at certain frequency ranges. However, high conductivity media often causes undesirable electrothermal effects.12 It should be also noted that selection of the buffer conductivity is restrictive in the case of biological samples, because excessive osmotic stress can cause cell damage.13 Thus, design and development of devices for specific applications require characterization of each ac electrokinetic mechanism over the desired range of electric field strength and buffer concentration. Alternating current electrokinetic forces and resultant motion of colloidal particles suspended in an aqueous medium have been investigated by many researchers to develop microfluidic devices for various applications. Approximate analytical series solutions to predict DEP forces exerted on colloidal particles are demonstrated in the case of the simple interdigitated electrode system, using Green’s functions14 and Fourier series.15 However, numerical simulation would be the most common method to analyze electric field and the electrokinetic forces induced by complex electrode (10) Huang, Y.; Mather, E. L.; Bell, J. L.; Madou, M. Anal. Bioanal. Chem. 2002, 372, 49. (11) Jones, T. B. J. Electrost. 2001, 51-52, 290. (12) Ramos, A.; Morgan, H.; Green, N. G.; Castellanos, A. J. Phys. D: Appl. Phys. 1998, 31, 2338. (13) Aldaeus, F.; Lin, Y.; Roeraade, J.; Amberg, G. Electrophoresis 2005, 26, 4252. (14) Wang, X.-J.; Wang, X.-B.; Becker, F. F.; Gascoyne, P. R. C. J. Phys. D: Appl. Phys. 1996, 29, 1649. (15) Morgan, H. A.; Izquierdo, G.; Bakewell, D.; Green, N. G.; Ramos, A. J. Phys. D: Appl. Phys. 2001, 34, 1553. 10.1021/ac7024859 CCC: $40.75

© 2008 American Chemical Society Published on Web 03/05/2008

geometries. Numerous results of detailed numerical simulations of microconcentrators, particle sorters and separators, mixers, and biosensors that utilize DEP and ac-EO are available in the literature.16-20 Numerical simulations require intensive computations, especially for the performance optimization process that considers variations in the electric field conditions and the device geometries. For device applications, it is important to figure out the basic constraints of electrokinetic manipulation and appropriate operating conditions for target species in the early design stages. Thus, efficient methods to describe the relationship between the applicable electric field conditions and ac electrokinetic transport of colloidal particles are required. Castellanos et al.21 presented a scaling analysis of particle dynamics and a summary of the type of fluid flow observed in a simplified system consisting of interdigitated electrodes, whereas Bahukudumbi et al.22 have shown modified scaling analysis in terms of electrokinetic velocities. The simple scaling law of electrokinetic forces with respect to system parameters was demonstrated as an effective tool for the prediction of the dominant transport mechanism without numerical calculations. However, different types of DEP (negative/positive DEP) and the variation of the DEP force magnitude were not represented effectively in previous studies, because the colloidal particle’s relative polarizability was not taken into account. For electrokinetic applications, different strategies are generally required for designing electric fields and devices as DEP characteristics change as a function of the relative polarizability of particles. Particles are attracted toward the electrodes’ edges for positive DEP, whereas negative DEP repels particles from the electrode surface. On the basis of the direction of the DEP force, the motion of colloidal particles can be induced in a specific direction by creating electric field maxima or minima at desired locations. Relative polarizability of the particle is a function of the material properties, electric field frequency, and conductivity of the suspending medium. Thus, specific DEP manipulation of colloidal particles should be considered within a limited range of electric field frequency and conductivity of the buffer solution. Relative polarizability of the buffer solution with respect to the electrodes is also important, because ac-EO and EP are restricted by the double layer polarization on the electrodes. Hence, a simple and reliable theoretical tool, which can effectively consider the polarizability variations and predict the resultant particle motion, is required to design and optimize ac electrokinetic devices. In this paper, we demonstrate an effective way of predicting the ac electrokinetic motion of colloidal particles in a microscale device. A modified scaling analysis is constructed by considering the relative magnitudes of ac electrokinetic motion (EP, DEP and ac-EO) and Brownian motion of colloidal particles on interdigitated microelectrodes, which have simple planar geometry and analytically obtained electric field. Dominant (16) Green, N. G.; Ramos, A.; Morgan, H. J. Electrostat. 2002, 56, 235. (17) Albrecht, D. R.; Sah, R. L.; Bhatia, S. N. Biophys. J. 2004, 87, 2131. (18) Erickson, D Microfluid. Nanofluid. 2005, 1, 301. (19) Gagnon, Z.; Chang, H.-C. Electrophoresis 2005, 26, 3725. (20) Tuval, I.; Mezic, I.; Bottausci, F.; Zhang, Y. T.; MacDonald, N. C.; Piro, O. Phys. Rev. Lett. 2005, 95, 236002. (21) Castellanos, A.; Ramos, A.; Gonza´lez, A.; Green, N. G.; Morgan, H. J. Phys. D: Appl. Phys. 2003, 36, 2584. (22) Bahukudumbi, P.; Everett, W. N.; Beskok, A.; Bevan, M. A.; Huff, G. H.; Lagoudas, D.; Ounaies, Z. Appl. Phys. Lett. 2007, 90, 224102.

transport mechanisms at a given electric field and material conditions are described using phase diagrams, and effects of a particle’s relative polarizability and the ionic concentration of buffer solution are explained. Then, the results are validated through parametric experiments for different kinds of colloidal particles (polymeric and metallic particles and biological species) at various electric field conditions. Dominant transport mechanisms of each particle with different polarization characteristics are observed and compared with the results of the scaling analysis. As a result, we have shown that the theoretical model can provide quantifiable information for ac electrokinetic motion of colloidal particles over broad ranges of electric field frequencies and amplitudes. METHODS AND MATERIALS Interdigitated gold electrodes with 30 µm spacing were deposited on microscope slides using conventional photolithographic techniques. A circular flow chamber (10 mm diameter) was constructed by placing a 1 mm thick O-ring spacer on the observation area, and it was covered with a microscope cover glass during the experiments. Three different samples were prepared with polystyrene and gold particles and Clostridium sporogenes bacterial spore (ATCC 3584). Fluorescent polystyrene particles of 1 µm (FluoSpheres, Interfacial Dynamics) were diluted with distilled water, which has a conductivity of 2.6 × 10-3 S/m measured via a conductivity meter (PHH-80MS, Omega). The particle concentration was adjusted to 1 × 108/mL approximately from a manufacturer’s solution. Gold particles of 800 nm (Bangs Laboratories) were diluted with deionized (DI) water (Simplicity, Millipore), and the ionic concentration of the solution was adjusted by adding 0.1 mM NaHCO3. C. sporogenes was stained with SYTO9 and propidium iodide (LIVE/DEAD BacLight, Invitrogen), and the sample was diluted with DI water to obtain a concentration of ∼107 spores/mL. Test solutions were then pippeted into the fluid chamber, and ac voltage up to 10 V peak-to-peak was supplied by a function generator (AFG 3102, Tektronix) in the frequency range of 0∼100 MHz. Particle motion was observed using an optical microscope (TE2000-U, Nikon) and a 10× objective (0.3 NA). Images were captured using software (Insight, TSI) and a CCD camera (PowerView1.4MP, TSI) with 1376 × 1040 pixel resolution (6.45 µm pixel size). RESULTS AND DISCUSSION Scaling Analysis. In the presence of a nonuniform ac electric field, colloidal particles suspended in an aqueous medium experience electrokinetic forces including EP, DEP, and hydrodynamic drag force due to the bulk fluid motion induced by ac-EO at a certain frequency range. In addition to electrical forces, the particles are also influenced by Brownian motion. Lateral motion of colloidal particle motion is generally driven by interaction of these forces, and precise analysis for each transport mechanism is required for manipulation of particles in microfluidic devices. To reduce the effort involved in detailed numerical simulations and to gain understanding for the order of magnitude of each transport mechanism, we developed a scaling analysis that predicts dominant forces in a microscale device based on the maximum displacement of colloidal particles on interdigitated microelectrodes. The scaling map results in prediction of the dominant transport mechanism at a given operational condition. It also enables production of phase diagrams that describe particle Analytical Chemistry, Vol. 80, No. 8, April 15, 2008

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2

Ω2 1 0V0 t Xac-EO ) Λ 8 ηr (1 + Ω2)2

Figure 1. Schematics of simplified electric field lines on interdigitated electrodes.

motion as functions of the electric field frequency, amplitude, and media conductivity. Alternating Current Electroosmosis. For coplanar parallel electrodes, shown in Figure 1, electric field distortion due to the top surface of the fluid chamber is negligible if the electrolyte is confined in a tall fluid chamber of height much greater than several electrode width and spacing. Then, the electric field between two electrodes can be assumed as half-circular lines near the electrode surface. The electrokinetic forces can be represented in simple analytical forms using this simplified electric field distribution. The fluid motion on interdigitated electrodes due to ac-EO was previously explained in a series of papers.23-25 The tangential ac electric field produces electroosmotic fluid velocity due to the potential drop across the double layer on the electrodes, which can be represented as25

uEO )

0 0 ∂ ∆φDEt ) Λ (|∆φDL|2) η 4η ∂r

(1)

where 0 and  are the absolute permittivity and relative permittivity of the medium, respectively, η is the viscosity, ∆φD and ∆φDL are the potential drop across the diffuse layer and the double layer, respectively, and Et is the tangential electric field. The capacitance ratio Λ is given by, Λ ) CS/(CS + CD), where CS is the capacitance of the Stern layer, and CD is the capacitance of the diffuse layer. CS ) 0.007 F/m2 is used based on the experimental result of impedance measurements.25 With expressions for resistance of the fluid and capacitance of the double layer, electric circuit analogy can be applied to model the double layer potential drop by26,27

∆φDL )

V0 2(1 + jΩ)

(2)

where V0 is the applied voltage, j)x-1, Ω ) Λω0πr/2σλD, ω is the radian frequency, σ is the conductivity of the fluid, and λD is the Debye length. Then, the resultant displacement due to acEO motion can be expressed as21 (23) Green, N. G.; Ramos, A.; Gonza´lez, A.; Morgan, H.; Castellanos, A. Phys. Rev. E 2000, 61, 4011. (24) Gonza´lez. A; Ramos, A.; Green, N. G.; Castellanos, A.; Morgan, H. Phys. Rev. E 2000, 61, 4019. (25) Green, N. G.; Ramos, A.; Gonza´lez, A.; Morgan, H.; Castellanos, A. Phys. Rev. E 2002, 66, 026305. (26) Ramos, A.; Morgan, H.; Green, N. G.; Castellanos, A. J. Colloid Interface Sci. 1999, 217, 420. (27) Morgan, H.; Green, N. G. AC Electrokinetics: Colloids and Nanoparticles; Research Studies Press: Hertfordshire, U.K., 2003.

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(3)

Alternating current electroosmotic displacement becomes zero as the nondimensional frequency Ω goes to zero or infinity, which represents a bell shaped function with both ends approaching zero. Dielectrophoresis. In the case of an electric field with constant phase, the time-averaged DEP force can be represented as28

FDEP ) 2π0a3 Re{K}∇|E|2

(4)

where a is the particle radius, E is the electric field, and K is the Clausius-Mossotti (CM) factor. For homogeneous particles suspended in a medium, the CM factor is given by

K(/p, /) )

/p - / /p + 2/

(5)

where / is the complex electric permittivity of the media, which can be represented as / )  - jσ/ω. Subscript p refers to the particle. The CM factor represents the effective polarizability of the particle with respect to the suspending medium, which is a strong function of the applied frequency. The value of Re{K} varies between +1 and -1/2. With dependence on the sign of Re{K}, particle motion is induced toward the electrode surface (positive DEP) or away from the electrodes (negative DEP). Figure 2 shows the variation of Re{K} as a function of the electric field frequency and ionic strength of the suspending medium for solid spherical dielectric particles with the parameters p ) 2.55,  ) 78.5, and σp ) 0.01 S/m. The sign of Re{K} is switched from positive to negative around the crossover frequency (∼2 MHz) for low conductivity buffer solution cases (10-5 S/m and 10-4 S/m). However, only negative Re{K} is observed in the whole frequency range for the high conductivity buffer case (10-1 S/m), which shows a limitation of positive DEP by the conductivity of the buffer solution. Because the DEP force is proportional to the gradient of the electric field, a small device scale and high operational voltage are required to amplify the DEP motion of the suspended particles. Because of the potential loss induced by electrode polarization, the actual potential supplied to the fluid can be expressed as27

Vfluid ) V0 - 2∆φDL ) V0

jΩ 1 + jΩ

(6)

With the utilization of the half circular electric field approximation (E ) Vfluid/πr) and assuming force balance with Stokes drag for small particles, characteristic DEP displacement can be represented as21

XDEP )

a20 β2V02 1 Re{K} t η 3π2 r3

(7)

(28) Jones, T. B. Electromechanics of Particles; Cambridge University Press: Cambridge, U.K., 1995.

Figure 2. Plot of the real part of the Clausius-Mossotti factor for a solid spherical dielectric particle at various medium conductivities (for p ) 2.55, σp ) 0.01 S/m, and  ) 78.5).

where β2 ) Ω2/(1 + Ω2). It can be observed that β goes to unity as Ω approaches infinity, and thus the effect of electrode polarization can be neglected for large Ω. Electrophoresis. For thin electrical double layers (a/λD . 1), dynamic mobility of spherical particles can be expressed as29

µd )

( )

0σp ωa2 G η ν

(8)

displacements induced by random Brownian motion in one dimension is given by21

XBrownian )

( ) kBT t 3πaη

1/2

(12)

Brownian Motion. With the use of the Stokes-Einstein relation (D ) kBT/6πaη), the expressions for characteristic

where kB is the Boltzmann constant and T is the temperature. From the expression of each transport mechanism, comparisons of maximum displacements were obtained for scaling analysis. Figure 3 shows the result of scaling analysis using 30 µm electrode spacing, 1 µm polystyrene particle properties, which are p ) 2.55, Fp ) 1050 kg/m3, and σp ) 0.01 S/m.30 The homogeneous particle model was used with the parameters,  ) 78.5, D ) 1 × 10-9 m2/s, F ) 1000 kg/m3, µ ) 1 × 10-3 N s/m2, V ) 10 V. Relative magnitudes of characteristic particle displacement for each transport mechanism were compared, and the dominant transport mechanism with the largest displacement magnitude was predicted, as shown Figure 3a. At conductivities less than 10-4 S/m (i.e., typical range of DI water), electrode polarization effects induce dominant ac-EO motion of the fluid at low frequencies (1∼10 kHz). However, positive DEP starts to dominate as frequency increases, and negative DEP becomes significant after the crossover frequency (about 2 MHz). At conductivity values more than 10-2 S/m, positive DEP disappears because polarizability of the particle is less than that of the medium and the CM factor is negative over the whole frequency range. The ac-EO and negative DEP motions are relatively small at low frequencies where only Brownian motion is dominant. As frequency increases, ac-EO and negative DEP become dominant consecutively. Figure 3b shows the magnitude of the particle displacement in log scale normalized by its maximum value to represent the difference in an order of magnitude. As seen on the results, EP displacement is not dominant for the whole range of interest. The maximum particle displacement occurs for acEO, and the Brownian motion is four orders of magnitudes smaller than the ac-EO motion. The dimensional values of ac-EO and DEP

(29) O’Brien, R. W. J. Fluid Mech. 1988, 190, 71.

(30) Green, N. G.; Morgan, H. J. Phys. Chem. B 1999, 103, 41.

where ζp is the zeta potential of the particle, ν is the kinematic viscosity, and G is a function that represents inertial effects of particle motion as a function of the Womersley number R ) a xω/ν and is given as29

G(R2) )

1 + (1 + j)R/x2 1 + (1 + j)R/x2 + j(R2/9)(3 + (Fp - F)/F)

(9)

where Fp and F are the density of the particle and medium, respectively. Electrophoretic displacement can be derived from particle velocity (uEP ) µdE) as

XEP )

( )( )

0σp ωa2 βV0 1 G sin(ωt) η ν πr ω

(10)

where (βV0/πr) is an approximation for the half circular electric field with potential drop due to the electrode polarization. The maximum electrophoretic displacement can be determined based on the amplitude of the oscillatory motion as

XEP )

( )( )

0σp βV0 ωa2 2 G η πr ν ω

(11)

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Figure 3. (a) Frequency-conductivity phase diagram for polystyrene particles. (b) Predictions of normalized particle displacement in a second as a function of the frequency and conductivity (normalized by the maximum, 1.62 × 10-2 m). Particle displacement due to ac-EO (c) and DEP (d). Homogeneous particle model was used with the parameters, p ) 2.55, σp ) 0.01 S/m, Fp ) 1050 kg/m3,  ) 78.5, D ) 1 × 10-9 m2/s, F ) 1000 kg/m3, µ ) 1 × 10-3 Ns/m2, V ) 10 V, a ) 0.5 µm, and r ) 15 µm.

displacements are plotted in parts c and d of Figure 3. These two motions are limited by the electrode polarization effect, which is a function of the nondimensional frequency Ω. From eqs 3 and 7, it can be seen that displacements of ac-EO and DEP go to zero as Ω approaches zero. Thus, both transport mechanisms become insignificant in the low frequency and high conductivity region, and Brownian motion dominates. It should be noted that the scaling map is generated to determine the dominant transport mechanisms based on the twodimensional electric field assumption. Thus, spatial variations for each transport mechanism, especially in three-dimensional cases, cannot be accounted for precisely. However, these results are still applicable in design of more complex electrode systems because the complicated geometry of the electrodes can be divided into several subregions with different characteristic lengths, allowing predictions of local colloidal motion. It also should be noted that electrokinetic manipulation of particles is not possible in some regions of the scaling maps due to electrolysis effects. We experimentally observed electrolysis at frequencies below 800 Hz and voltages above 1 V. To avoid electrode damage, experimental validations of the scaling maps described in the next section were conducted outside the electrolysis range. We also observed that electrothermal effects were insignificant in the ranges of experiments (∼10 V). However, electrothermal effects can possibly dominate colloidal motion at higher voltage inputs, especially for cases with high conductivity buffers, because the power dissipation is directly proportional to 2836 Analytical Chemistry, Vol. 80, No. 8, April 15, 2008

the conductivity (W ∼ σE2).12 Although theoretical expressions are available, electrothermal effects are essentially related with three-dimensional flow motions and a different characteristic length scale is required to include electrothermal motions to the scaling analysis.21 Thus, explicit comparisons with other ac electrokinetic forces are not attempted in the presented study. Experimental Validations. The theoretical results are validated through experimental observations of particle motion utilizing interdigitated microelectrodes with 30 µm spacing. Three different types of particles, 1 µm polystyrene particles (polymer), 800 nm gold particles (metal), and C. sporogenes bacterial spores (biological species), were tested for examining the effect of polarizability of each particle. Randomly dispersed particles in the initial state were started with, and a steady-state distribution of the particles was observed in each case after applying electric fields. The dominant transport mechanism was determined based on the particle distribution and was compared with the scaling analysis. Properties of the particles and ionic solutions that were used in the scaling analysis are summarized in Table 1. Figure 4 shows the results of scaling analysis for 1 µm polystyrene particles with experimental observations of particle motion suspended in distilled water, which has a conductivity of 2.6 × 10-3 S/m. A random distribution of particles inside the fluid chamber was established in the initial state by feeding a fresh particle solution for each case. After application of a 10 V peakto-peak ac electric field for 5 min at specified frequencies, the steady-state distribution of the particles was captured. Each test

Table 1. Properties of Colloidal Particles and Ionic Solutions Used in the Scaling Analysis particle diameter conductivity (σp) buffer solution

polystyrene

gold

1 µm 10-2 S/m

800 nm 4.9 × 107 S/m

distilled water

NaHCO3 (0.1 mM)

C. sporogenes 1 µm 10-2 S/m DI water, NaCl (0.1 and 1 mM)

conductivity (σ) 2.6 × 10-3 S/m 1.8 × 10-3 S/m 1.0 × 10-5 S/m 1.3 × 10-3 S/m 1.3 × 10-2 S/m diffusivity (D) 10-9 m2/s viscosity (η) 10-3 N s/m2

case is indicated on the phase diagram and the particle displacement map, as shown in parts a and b of Figures 4. Scaling maps are plotted in a frequency-conductivity plane to demonstrate the transition of the dominant transport mechanism as a function of these two parameters. Effects of other parameters can be explained on scaling maps in different planes. We also observed the voltage dependence of the dominant transport mechanism utilizing a voltage-frequency phase diagram for the same buffer conductivity and found that the transition is dependent only on the applied frequency, with the exception of low voltage regions (less than 1 V) where Brownian motion was mostly dominant. As predicted from the scaling analysis, transition of the dominant transport mechanism can be seen on the experimental results,

presented in Figure 4c. Alternating current electroosmotic motion was observed at 1 kHz (case 1), where a large amount of particles were concentrated on the center of the electrode surface, as predicted by the scaling analysis in Figure 4a. With increased frequency, the particles were forced to move toward the electrode gap and concentrated on the edges of the electrodes by positive DEP motion. The strength of positive DEP was increased as the frequency was gradually increased up to 100 kHz (cases 2, 3, and 4). However, the DEP motion was decreased at 1 MHz (case 5). The increase in positive DEP till 100 kHz frequency can be explained with a decrease of ac-EO motion, which competes with the positive DEP force. As seen in Figure 3c, ac-EO motion decreases as the frequency increases over 10 kHz at a conductivity of 2.6 × 10-3 S/m. Because the positive DEP and ac-EO are effective in opposite directions, positive DEP increases as ac-EO decreases. In case 2, small amounts of particles were observed on the center of the electrode surface, whereas positive DEP motion was dominant on the electrode gap. This can be interpreted as a result of competition between the ac-EO motion of the bulk fluid and the positive DEP, where ac-EO motion is affecting the particle transport far from the electrode edges at 10 kHz frequency. Although the scaling map predicts the ac-EO dominant transport of particles at 10 kHz frequency, positive DEP is effective near the electrode gap. In order to obtain more precise theoretical predictions near the region where ac-EO and DEP are balanced, further correlations with the experimental results for ac-EO motion by deriving an empirical value of capacitance ratio, Λ, in eq 1

Figure 4. (a) Frequency-conductivity phase diagram for 1 µm polystyrene particles. (b) Normalized particle displacement as a function of frequency and conductivity with loci of six experimental results (normalized by the maximum displacement of 1.62 × 10-2 m). (c) Steady-state distribution of 1 µm polystyrene particles suspended in distilled water (2.6 × 10-3 S/m) after applying a 10 V peak-to-peak ac electric field for 5 min at specified frequencies. For image 1, concentrated particles on the center of the electrode surface driven by the ac-EO mechanism are also shown. Because of the nature of negative DEP that repels particles away from the electrode surface, the particles for case 6 were sedimented for 3 h to capture the lateral motion of particles at the image focal plane.

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Figure 5. (a) Voltage-frequency phase diagram for the 800 nm gold particles. (b) Normalized particle displacement as a function of voltage and frequency with loci of nine experimental results (normalized by the maximum displacement of 1.72 × 10-3 m). (c) Steady-state distribution of 800 nm gold particles suspended in 0.1 mM NaHCO3 buffer solution (1.8 × 10-3 S/m) after applying the specified ac electric field for 15 s.

Figure 6. (a) Normalized particle displacement for 800 nm gold particles as a function of voltage and frequency with loci of nine experimental results (normalized by the maximum displacement of 1.90 × 10-2 m). (b) Steady-state distribution of 800 nm gold particles suspended in 0.1 mM NaHCO3 buffer solution (1.8 × 10-3 S/m) after applying the specified ac electric field for 15 s.

would be required. Decrease of positive DEP near the crossover frequency (about 2 MHz) and negative DEP motion of particles at 10 MHz are well captured by cases 5 and 6. Because of the nature of negative DEP that repels particles away from the electrode surface, particles for case 6 were sedimented for 3 h prior to the experiments, which enabled observation of lateral motions at the focal plane of the image. Figure 5 shows theoretical and experimental results for 800 nm gold particles suspended in 0.1 mM NaHCO3 buffer solution. Images were captured after applying an electric field at a specified frequency and voltage for 15 s. Figure 5a,b shows a theoretically predicted dominant force map in the frequency-voltage phase 2838 Analytical Chemistry, Vol. 80, No. 8, April 15, 2008

plane at buffer conductivity of 1.8 × 10-3 S/m and normalized maximum displacement of particles in the log scale. As shown in the figure, only ac-EO and positive DEP appear as dominant transport mechanisms except in the low voltage region where Brownian motion is dominant. Unlike the polymeric particles, polarizability variation of gold particles is negligible due to its higher conductivity (4.9 × 107 S/m) compared to that of the buffer solution. Therefore, only a positive DEP force appears over 50 kHz. Figure 5c shows experimental results consistent with the scaling map. At 1 kHz frequency (cases 1, 4, and 7), the particles were driven to the center of the electrode by ac-EO motion. The strength of the ac-EO motion was increased with

Figure 7. (a) Frequency-conductivity phase diagram for C. sporogenes spores. Particle displacement normalized by the maximum displacement of 1.62 × 10-2 m (b), and dielectrophoretic displacement (c) for C. sporogenes as a function of frequency and conductivity with loci of six experimental results. (d) Steady-state distribution of C. sporogenes spores suspended in buffer solutions with various conductivities after applying ac electric fields at specified electric field frequencies for 1 min. The ionic strength of the buffer solution was varied by adjusting the molarity of the NaCl solution.

increased voltage, and more particles were concentrated on the center of the electrode. For frequencies higher than 1 kHz, particles were concentrated on the edges of the electrodes due to positive DEP motion. For cases 2 and 3, weak positive DEP motion was observed near the electrode gap, while Brownian motion was observed away from the electrodes as predicted in the phase diagram. With increased voltage, more particles were concentrated and pearl chains of particles were formed between the electrodes. Figure 6 shows results of continued experiments using 800 nm gold particles under higher frequencies and voltages. Positive DEP progressively disappears as frequency reached 100 MHz, and only weak positive DEP motion was observed for the 10 V voltage (case 9), whereas the scaling map does not predict the decrease of positive DEP at the highfrequency range. It can be conjectured that such high-frequency electric fields do not provide enough time for relaxation of the induced dipole moment on gold particles, and thus overall effective dipole is reduced due to dielectric loss. The characteristic relaxation time of polarization is dependent on the chemical composition and structure of the materials and the temperature.31

Thus, in order to predict the decrease of positive DEP by considering dielectric loss at high frequencies, more detailed models of complex electric permittivities of the particle and buffer solution would be required. Figure 7 shows theoretical and experimental results for C. sporogenes bacterial spores suspended in ionic solutions with various conductivities. Conductivity of the suspending medium was varied by adjusting the molarity of the NaCl solution, and images were captured after applying a 10 V electric field at various frequencies for 1 min. In the case of biological species, an effective description of particle polarizability is required due to the variations in particle size and shape and complex inner structure of the species. For nonhomogeneous particles, the layered shell model can be used to describe the particle polarizability simply by using uniform dielectric properties for each layer.27 However, it is usually difficult to develop a detailed model, which includes the effects of size and shape variations, and species specific dielectric parameters for bacterial spores. In order to reduce the (31) Bottcher, C. J. F. Theory of Electric Polarisation; Elsevier Press: London, U.K., 1952.

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Figure 8. (a) Normalized particle displacement for C. sporogenes as a function of voltage and frequency with loci of eight experimental results (normalized by the maximum displacement of 3.30 × 10-2 m). (b) Steady-state distribution of C. sporogenes spores suspended in DI water (10-5 S/m) after applying the specified ac electric field for 1 min.

time for detailed modeling, we approximated bacterial spores to have a spherical shape with a 1 µm average diameter and used a simple solid model for describing the spore’s behavior based on experimental observations. C. sporogenes spores have shown scalable motion with the frequency and amplitude of the electric field, without a second crossover in the DEP spectra within the 1 kHz to 100 MHz range. This initial observation of DEP characteristics allowed simple correlation of scaling analysis for spores with the experiments based on a crossover frequency measurement.30 Figure 7a,b shows the theoretically predicted dominant force and normalized maximum displacement in the frequencyconductivity phase plane. For the low-conductivity solution (10-5 S/m), the theoretical result shows a decrease of ac-EO strength and transition to dominant positive DEP motion near the 1 kHz frequency (case 1) and predicts positive DEP dominance at 50 kHz (case 4). Consistent experimental results are demonstrated in Figure 7d. In case 1, positive DEP and ac-EO motion of spores are captured at the electrode gap and on the electrode surface, respectively. This can be interpreted as the transition of the dominant force from ac-EO to positive DEP. For the result with 0.1 mM NaCl buffer solution, dominant ac-EO motion is observed at 1 kHz (case 2), and the strength of ac-EO is decreased at 50 kHz (case 5). The transition to dominant positive DEP motion is predicted for case 5 in the phase diagram. However, positive DEP motion of the spores on the electrode gaps, such as in case 1, is not observed, because the strength of positive DEP is decreased as the conductivity is increased, as shown in Figure 7c. In the case of the 1 mM NaCl buffer solution, case 3 shows a decrease of spore concentration on the electrode surface, and the strength of ac-EO motion is decreased compared with the 0.1 mM case (case 2) as predicted in the scaling map. At 50 kHz (case 6), it can be seen on the image that ac-EO motion is considerably reduced and only a few spores are driven away from the electrode edges. This decrease of ac-EO strength in case 6 deviates from the theoretical result, which predicts increased acEO motion compared with case 5. In order to obtain accurate theoretical results for ac-EO motion, capacitance parameters (CS, CD) should be correlated with the actual response of the double layer. We plan further studies to determine capacitance values of the double layer by analyzing impedance characteristics of the system, especially for high-conductivity buffer cases where the capacitance of the diffuse layer is significant. 2840

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Experimental validation of the scaling map was continued for the spores suspended in DI water with various electric frequencies and voltages, as shown in Figure 8. Figure 8a shows the scaling map of normalized displacement with the frequency-voltage phase plane. It can be seen that ac-EO, positive DEP, and negative DEP progressively dominate the motion of the spores as frequency increases, whereas the overall magnitude of spore motion is increasing with the applied electric field. Experimental results, shown in Figure 8b, demonstrate strong positive DEP at 1 kHz (cases 1 and 5), while positive DEP decreases as the frequency approaches to the crossover value (∼2 MHz). At 10 MHz (cases 4 and 8), spore concentration cannot be observed at the focal plane due to the onset of negative DEP, which has been predicted by the scaling map. Thus, most of the spores were repelled from the electrode surface, and concentration of spores could not be achieved at the focal plane of observation. CONCLUSIONS A theoretical predictive tool for ac electrokinetic manipulation of micrometer sized particles in a microfluidic device has been presented. With the utilization of a scaling analysis that considers relative magnitudes of EP, DEP, ac-EO, and Brownian motion, dominant transport mechanisms and their orders of magnitudes were explained over broad ranges of electric field frequency, amplitude, and ionic strength of the suspending medium. The resultant theoretical model was validated through parametric experimental examination of different types of colloidal particles including polymer (polystyrene), metal (gold), and biological species (C. sporogenes bacterial spores) with interdigitated electrodes. The ac electrokinetic motion of colloidal particles at various conditions of the electric field and suspending medium were well described in a predictive manner. Quantitative information of ac electrokinetic mechanisms for target species and media over a broad range of electric field frequency and amplitude enables configuration of the required electric field in the early design stages and provides an easy way to design frequency specific manipulations of various colloidal particles suspended in aqueous media without detailed numerical simulations. Therefore, the presented model can be applied in the design and optimization of future ac electrokinetic devices in an effective way.

ACKNOWLEDGMENT The authors thank Martha Cepeda and Dr. Suresh D. Pillai for providing the samples of bacterial spores. This research was supported by the United States Department of Homeland Security through the National Center for Food Protection and Defense (NCFPD), Grant Number N-00014-04-1-0659. However, any opinions, findings, and conclusions or recommendations in this

document are those of the authors and do not necessarily reflect the views of the U.S. Department of Homeland Security.

Received for review December 6, 2007. Accepted January 28, 2008. AC7024859

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